# New global logarithmic stability of the Cauchy problem for elliptic equations

## TL;DR

This paper establishes a new global logarithmic stability estimate for the Cauchy problem associated with anisotropic elliptic equations in Lipschitz domains, enhancing understanding of solution stability in inverse problems.

## Contribution

It introduces a novel global logarithmic stability result for the Cauchy problem of elliptic equations, combining techniques from previous stability and inverse medium problem studies.

## Key findings

- Proves a global logarithmic stability estimate for the Cauchy problem
- Utilizes combined techniques from existing stability and inverse problem methods
- Enhances theoretical understanding of elliptic PDE stability

## Abstract

In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to establish stability estimate for the Cauchy problem [4] (see also [1]) combined with tools we already used in [6] to study an inverse medium problem.